Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Chaotic balanced state in a model of cortical circuits
Neural Computation
Spiking Neuron Models: An Introduction
Spiking Neuron Models: An Introduction
Dynamics of the firing probability of noisy integrate-and-fire neurons
Neural Computation
Integrate-and-fire neurons driven by correlated stochastic input
Neural Computation
Temporal correlations in stochastic networks of spiking neurons
Neural Computation
Spontaneous Dynamics of Asymmetric Random Recurrent Spiking Neural Networks
Neural Computation
Stationary Bumps in Networks of Spiking Neurons
Neural Computation
Noise in Integrate-and-Fire Neurons: From Stochastic Input to Escape Rates
Neural Computation
Systematic fluctuation expansion for neural network activity equations
Neural Computation
| Hi-index | 0.00 |
We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution, mean rate, variance, and autocorrelation function of the network activity. The model is applicable to any network where the probability of firing of a neuron in the network depends on only the number of neurons that fired in a previous temporal epoch. Networks with statistically homogeneous connectivity and membrane and synaptic time constants that are not excessively long could satisfy these conditions. Our model completely accounts for the size of the network and correlations in the firing activity. It also allows us to examine how the network dynamics can deviate from mean field theory. We show that the model and solutions are applicable to spiking neural networks in biophysically plausible parameter regimes.